Yes, both has happened in history of Bollywood movies.
Deleted scenes typically happen when length of movie is more and editor chops some portions to keep the length and pace to match expectations. Sometimes, censor board asks removal of portions which again become deleted scenes. Let me give few examples that I know of. Many such scenes later surface on social media sites like Facebook, You Tube etc.
Alternate endings meanwhile is like either to keep audience happy (sometimes 2 heroes of equal value or stardom need to win, so to test audience film makers do this; for few film makers, this is a creative experimentation as they may feel 1 climax say good/sad may not be ultimate as they can envision more climax scenes or how to end the movie to cater to different sects of audiences).
DELETED SCENES
Dilwale Dulhania Le Jayenge (1995): This movie had extended train chase scene which is still available on the special edition DVD of the movie. Due to its length and minimal impact, it was deleted from the movie
Kabhi Khushi Kabhie Gham (2001): More character interactions from Rahul played by Shah Rukh Khan were removed as editors and Karan Johar felt the narrative tightness/clarity would get affected if not deleted as it was a huge star cast and many members already in the movie. These were already filmed in London but removed from the movie.
Ra.One (2011): As per reports, Multiple action sequences and alternate robot fight choreography were removed (some replaced by CGI shots)
Bajirao Mastani (2015): Some of the intimate palace court scenes were removed considering censorship rules in India and the film maker did not want further disputes for the release.
Alternative endings
Kuch Kuch Hota Hai (1998): There was an ending planned where Rani Mukherji’s Tina was alive (that would have been some twist). But due to audience emotion, this was changed so SRK and Kajol would be together. Till 2000’s nobody wanted hero to be with more than 1 girl at the same time (or vice versa)
Taal (1999): This movie is 1 of my personal favourites for the A R Rahman magic and it even had more elaborate musical montage in the original recording and movie. This was shortened for theatrical release while exists on original footage as an extended cut/ alternate ending